Normalized solutions of one-dimensional defocusing NLS equations with nonlinear point interactions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910147516825600 |
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| author | Barbera, Daniele Boni, Filippo Dovetta, Simone Tentarelli, Lorenzo |
| author_facet | Barbera, Daniele Boni, Filippo Dovetta, Simone Tentarelli, Lorenzo |
| contents | We investigate normalized solutions for doubly nonlinear Schrödinger equations on the real line with a defocusing standard nonlinearity and a focusing nonlinear point interaction of $δ$-type at the origin. We provide a complete characterization of existence and uniqueness for normalized solutions and for energy ground states for every value of the nonlinearity powers. We show that the interplay between a defocusing standard and a focusing point nonlinearity gives rise to new phenomena with respect to those observed with single nonlinearities, standard combined nonlinearities, and combined focusing standard and pointwise nonlinearities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21700 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normalized solutions of one-dimensional defocusing NLS equations with nonlinear point interactions Barbera, Daniele Boni, Filippo Dovetta, Simone Tentarelli, Lorenzo Analysis of PDEs Mathematical Physics 35Q40, 35Q55, 35R06, 49J40 We investigate normalized solutions for doubly nonlinear Schrödinger equations on the real line with a defocusing standard nonlinearity and a focusing nonlinear point interaction of $δ$-type at the origin. We provide a complete characterization of existence and uniqueness for normalized solutions and for energy ground states for every value of the nonlinearity powers. We show that the interplay between a defocusing standard and a focusing point nonlinearity gives rise to new phenomena with respect to those observed with single nonlinearities, standard combined nonlinearities, and combined focusing standard and pointwise nonlinearities. |
| title | Normalized solutions of one-dimensional defocusing NLS equations with nonlinear point interactions |
| topic | Analysis of PDEs Mathematical Physics 35Q40, 35Q55, 35R06, 49J40 |
| url | https://arxiv.org/abs/2503.21700 |